where \(G_N\)  is the Newton constant, whereas \(m\)  and \(r\)  are the typical masses and separations of the system, respectively. By taking this relation into account, PN corrections guarantee that the system is bounded by its own gravity, and corrections are organized such that at \(n\) -PN order they scale as: \(G_N^{n-l}v^{2\ell }\)  where \(0\le \ell \le n-1\) . This method has been developed by Einstein in 1916 [1]}, and the 1PN corrections to the Newtonian potential where computed already in 1917 by Lorentz and Droste. The evaluation of higher order PN corrections is far from effortless[2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, and it took decades to obtain the 4PN corrections, evaluated in 2014 [7]}.
